Math 30-1: Alberta Curriculum & Diploma Prep

Math 30-1 curriculum: 7 units, 50 lessons (Alberta Mathematics 30-1)

Unit 1: Function Transformations

• Function Foundations, Refresh function notation, domain and range, and how to evaluate f(x) — the groundwork every Math 30-1 unit builds on.
• Piecewise Functions, Graph functions defined by different rules on different intervals, and evaluate them by picking the right piece for each x-value.
• Sums & Difference of Functions, Build h(x) = f(x) + g(x) or f(x) - g(x), sketch the combined graph, and state the domain the two functions share.
• Products & Quotients of Functions, Multiply and divide functions, then pin down the new domain — especially where a quotient's denominator hits zero.
• Composite Functions, Evaluate and simplify compositions like f(g(x)) by working from the inside out — a skill the diploma exam leans on heavily.
• Horizontal & Vertical Translations, Slide graphs left, right, up or down with y - k = f(x - h), and write the equation of a shifted graph from its picture.
• Reflections & Stretches, Reflect graphs in the x-axis or y-axis and stretch them by a factor, predicting which points move and which stay fixed.
• Combining Transformations, Apply stretches, reflections and translations in the right order to sketch y = af(b(x - h)) + k from a base graph.
• Inverse Functions, Swap x and y to find an inverse algebraically, sketch its reflection in the line y = x, and restrict a domain so the inverse is a function.

Unit 2: Polynomial Functions

• Characteristics of Polynomial Functions, Read degree and leading coefficient to predict end behaviour and the possible numbers of x-intercepts and turning points.
• Dividing Polynomials, Divide polynomials using long and synthetic division, and connect each remainder to the remainder theorem.
• Factoring & the Factor Theorem, Test whether x - a is a factor by checking if P(a) = 0, then combine the factor theorem with division to factor cubics and quartics.
• Zeros, Roots & x-Intercepts, Connect three names for one idea — a zero of P(x), a root of P(x) = 0, and an x-intercept — and describe repeated zeros using multiplicity.
• Graphing Polynomial Functions, Sketch cubics, quartics and quintics from factored form, using intercepts, multiplicity and end behaviour as your guide.
• Polynomial Equations & Inequalities, Solve polynomial equations by factoring, then use a sign analysis or the graph to handle inequalities like P(x) > 0.
• Solving Problems with Polynomial Functions, Model volume, area and other quantities with polynomials, then solve for the dimensions that meet a given condition.

Unit 3: Exponents & Logarithms

• Review of Exponent Laws, Sharpen the product, quotient and power rules, plus negative and rational exponents, before exponential functions arrive.
• Exponential Functions & Their Graphs, Graph exponential growth and decay like y = 2^x and y = (1/2)^x, identifying the y-intercept and horizontal asymptote.
• Introduction to Logarithms, Meet the logarithm as the inverse of an exponential — convert between log and exponential form, and evaluate simple logs mentally.
• Transformations of Logarithmic Functions, Shift, stretch and reflect logarithmic graphs, and track how each transformation moves the vertical asymptote.
• Laws of Logarithms, Expand and condense log expressions using the product, quotient and power laws — the algebra behind solving log equations.
• Solving Exponential Equations, Solve equations like 3^(2x) = 7 by matching bases when possible and taking a logarithm of both sides when not.
• Solving Logarithmic Equations, Use log laws to collapse each side into a single logarithm, solve, and reject roots that make any argument negative or zero.
• Applications of Exponential & Log Functions, Model compound interest, half-life and population growth — the applications this unit builds toward on the diploma exam.

Unit 4: Trigonometric Functions

• Angles in Standard Position & Radian Measure, Convert fluently between degrees and radians and sketch angles in standard position — the language of Math 30-1 trigonometry.
• The Unit Circle, The unit circle links angles to coordinates — memorize special angles like π/6 and π/4 and read exact trig values straight off the circle.
• The Six Trigonometric Ratios, Define sine, cosine and tangent along with their reciprocals — cosecant, secant and cotangent — and evaluate all six for any angle.
• Coterminal Angles & Reference Angles, Find the reference angle in every quadrant and generate coterminal angles by adding or subtracting full rotations of 2π.
• Graphs of Sine & Cosine Functions, Sketch sine and cosine waves, reading amplitude, period, phase shift and midline straight from y = a sin b(x - c) + d.
• Graphs of Tangent & Reciprocal Trig Functions, Graph tangent with its period of π and its vertical asymptotes, then build cosecant, secant and cotangent from their reciprocal definitions.
• Transformations of Trig Functions, Stretch, shift and reflect sinusoidal graphs, and write an equation that matches a given wave from its features.
• Applications of Trig Functions, Fit sinusoidal models to Ferris wheels, tides and other periodic motion, then interpret amplitude and period in context.

Unit 5: Trigonometric Identities

• Equivalent Trigonometric Expressions, Rewrite trig expressions in equivalent forms, simplifying with known identities and stating non-permissible values.
• Reciprocal & Quotient Identities, Turn tangent into sine over cosine and secant into one over cosine, applying quotient and reciprocal identities to simplify.
• Pythagorean Identities, Work with sin²x + cos²x = 1 and its rearrangements to simplify expressions and trade one trig ratio for another.
• Sum & Difference Identities, Break angles apart with formulas like sin(A + B) to find exact values for angles such as 15° that sit off the unit circle.
• Double Angle Identities, Apply sin 2x = 2 sin x cos x and the three forms of cos 2x to collapse expressions that mix single and double angles.
• Proving Trigonometric Identities, Prove identities by working each side independently — pick a side, convert to sines and cosines, and simplify until both match.
• Solving Trigonometric Equations, Solve trig equations exactly over the interval from 0 to 2π, then write general solutions that capture every rotation.

Unit 6: Radical & Rational Functions

• Radical Functions & Transformations, Graph y = √x and its transformations, tracking how the endpoint moves and why the domain stops where the radicand turns negative.
• Solving Radical Equations, Square both sides to clear a radical, then test every answer — squaring can create extraneous roots that fail the original equation.
• Reciprocal Functions, Sketch y = 1/f(x) from the graph of f, sending zeros of f to vertical asymptotes and keeping invariant points where y = ±1.
• Rational Functions & Asymptotes, Locate vertical, horizontal and oblique asymptotes from a rational function's equation, and tell true asymptotes apart from holes.
• Oblique Asymptotes & End Behaviour, Divide numerator by denominator to find an oblique asymptote, then describe how the curve hugs that line as x grows without bound.
• Graphing Rational Functions, Combine intercepts, asymptotes and behaviour on each side of them into a complete, accurate sketch of a rational function.
• Solving Rational Equations & Applications, Clear denominators to solve rational equations, watch for non-permissible values, and apply the method to rate and work problems.

Unit 7: Permutations & Combinations

• Fundamental Counting Principle & Factorials, Count multi-stage outcomes by multiplying the choices at each step, and simplify factorial expressions like n!/(n - 2)!.
• Permutations, Arrange objects where order matters — compute nPr for lineups and codes, including arrangements of words with repeated letters.
• Combinations, Choose groups where order does not matter — evaluate nCr for committees and hands, and see why it divides out the repeated orderings.
• Pascal's Triangle & the Binomial Theorem, Expand powers like (x + y)^n with the binomial theorem, using Pascal's triangle or nCr to find any coefficient or general term.

Frequently asked questions

What's on the Math 30-1 diploma exam?

The Math 30-1 diploma exam tests the full course: Function Transformations, Polynomial Functions, Exponents & Logarithms, Trigonometric Functions, Trigonometric Identities, Radical & Rational Functions, Permutations & Combinations. It's machine-scored, multiple choice and numerical response, and counts for 30% of your final Math 30-1 grade, with the other 70% coming from your school mark.

Is Math 30-1 hard?

For most students, Math 30-1 is Alberta's toughest high-school math course, it moves quickly through pre-calculus topics and ends in a diploma exam. It's very manageable with steady work: keep up unit by unit, practice exam-style questions, and get help the moment something stops making sense.

Do I need Math 30-1 or Math 30-2?

It depends on your post-secondary plans. Math 30-1 is the pre-calculus route and is required for programs that lead to calculus, engineering, computer science, and most sciences. Math 30-2 satisfies programs that don't require calculus. Check the admission requirements for the programs you're considering before you choose.

How many units are in Math 30-1?

Math 30-1 on Studyio has 7 units: Function Transformations, Polynomial Functions, Exponents & Logarithms, Trigonometric Functions, Trigonometric Identities, Radical & Rational Functions, Permutations & Combinations. That's 50 lessons in total, matching the Alberta curriculum from the first unit through exam review.

Is Studyio aligned to the Alberta curriculum?

Yes. Every Math 30-1 lesson on Studyio follows the Alberta Program of Studies: the same units, in the same order, they're taught in class. The course has 7 units and 50 lessons, each with a voice-over walkthrough, worked examples, and a practice quiz with step-by-step solutions.

Is Studyio free?

Yes. Studyio is free to start, with no credit card required. The free plan includes lesson access, unlimited quizzes, and step-by-step solutions. Pro, $7.99 a month or $73.99 a year after a 7-day free trial, unlocks unlimited Alberta Diploma Exam practice and unlimited help from Ms. Emma, Studyio's AI tutor.